global environmental standards with heterogeneous polluters
TRANSCRIPT
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International Review of Economics and Finance, forthcoming
Global Environmental Standards with Heterogeneous Polluters
Ting Levy* Elias Dinopoulos
Florida Atlantic University University of Florida
Current Version: December 18, 2015
Abstract: We introduce environmental quality standards into a model of intra-industry trade with heterogeneous
polluters. Pollution stems from consumption and pollution intensity declines with product-specific environmental
quality. We formally analyze the effects of environmental standards and trade liberalization on intra-industry
trade patterns, pollution, and welfare. Trade liberalization takes the form of lower per-unit trade costs, lower fixed
foreign-market entry costs, or greater number of trading partners. When consumer preferences for environmental
quality are weak (strong) relative to the environmental quality elasticity of production costs, firms discovering
dirtier (cleaner) products are more profitable and engage in exporting. More stringent environmental standards or
trade liberalization policies enhance per-capita real consumption. The effects of these policies on global pollution
and welfare are ambiguous.
JEL Classification: Q48, Q53 and L91
Key words: intra-industry trade; firm heterogeneity; environmental standards; environmental R&D.
___________________________
* Ting Levy: Department of Economics, Florida Atlantic University, Boca Raton, Florida, 33431. E-mail:
[email protected]; Tel: (352) 672-7301. Elias Dinopoulos: Department of Economics, University of Florida,
Gainesville, FL 32611. E-mail: [email protected]; Tel: (352) 392-8150.
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1. Introduction
The nexus between trade and the environment has generated an intense academic and policy debate.1
Despite the large body of theoretical and empirical literature, the channels through which international trade
influences environmental quality are not well understood. Consider, for instance, the effects of tougher
environmental standards on international competitiveness and global pollution. On the one hand, Porter (1991)
and Porter and Van der Linde (1995) argue that tough environmental standards trigger environmentally friendly
technological innovations that may reduce global pollution and enhance international competitiveness. On the
other hand, Palmer et al. (1995), citing survey evidence argue that the costs of environmental regulations exceed
their benefits implying that environmental regulations harm international competitiveness.
Similar considerations apply to several other controversial hypotheses concerning the effects of
globalization on the environment. According to the “race to the bottom” hypothesis, import competition from
countries with low environmental standards puts pressure for less stringent environmental regulations in countries
with high environmental standards; the “pollution heaven hypothesis” asserts that countries with low
environmental standards become destinations of multinationals using pollution-intensive technologies leading to
higher global pollution; and the “gains from trade” hypothesis states that openness encourages growth and
innovation both of which could improve environmental quality.
The aforementioned arguments have been developed using traditional static and dynamic trade models
generating inter-industry trade based on comparative advantage (Bovenberg and Smulders, 1995; Brock and
Taylor, 2005; Chao and Yu. 2007). A few studies have addressed environmental issues in open economies
engaging in intra-industry trade generated by symmetric monopolistically competitive firms (Gurtzgen and
Rauscher, 2000; Fung and Maechler, 2005; Haupt , 2006;), or multi-country models with trade costs generating
Ricardian trade under perfect competition (Erdogan, 2014).
The present paper studies formally the impact of environmental standards and globalization in an
economic environment characterized by environmental-quality heterogeneity. It is partially motivated by the
global automobile industry which constitutes a major source of air pollution.2 The global automobile industry
features substantial intra-industry trade and product-specific heterogeneity in environmental quality.3
1 Frankel (2009) offers an excellent overview of the literature addressing the environmental effects of trade.
2 Emissions, such as air toxics and urban smog, contribute substantially to health and environmental degradation.
Additionally, a typical consumer’s most polluting daily activity is car driving. On average, each car generates 20 pounds of
CO2 per gallon burned leading to 6 to 9 tons of CO2 emissions each year. For a typical household in the United States, vehicle
emissions contribute to 51% of CO2, followed by household appliances (26%), and heating and cooling (18%). 3 Cars with different fuel efficiency deliver different amounts of emissions. For instance, among 2014 models, Chevrolet
Spark EV delivers 119 miles per gallon whereas Mercedes-Benz SLS delivers 14 miles per gallon. Many countries including
the United States, Japan and Germany export and import cars and trucks from each other. Feenstra and Taylor (2014, Table
6-4) report that in 2012 the value of intra-industry index for small cars was 40 percent.
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Environmental standards on vehicle emissions constitute an important national and global policy tool used to
improve air quality. These environmental quality standards are expressed as minimum fuel efficiency
requirements in the United States or maximum CO2 emissions in Europe.4 Finally, the global character of the
automobile industry has generated international cooperation leading to a global harmonized emission standard.
Investment in environmental R&D is common in U.S. manufacturing industries and accounts for a sizable
share of R&D. Scott (2003) surveys a group of manufacturing companies and reports that, on average, 23.9% of
firm R&D expenditures are channeled towards environmental projects. Moreover, over one-half of the firms
participating in the survey indicate that environmental R&D projects are undertaken because of specific
environmental legislation. Goldberg (1998) confirms this finding by arguing that Corporate Average Fuel
Economy Standards (CAFE) regulation offers incentives to develop environmentally friendlier technologies and
vehicles.
In this paper we propose a model of intra-industry trade with heterogeneous polluters and structurally
symmetric countries to address the following questions. What determines environmental-quality heterogeneity
within each industry and the environmental content of intra-industry trade? Do more stringent global
environmental standards lower industry productivity and competitiveness? What are the effects of higher
environmental standards and trade liberalization on global consumption-based pollution, and welfare?
Following the theory of trade with heterogeneous firms, we envision a global economy consisting of
many structurally identical countries with labor as the sole factor of production.5 We are the first to recognize that
the assumption of structurally identical countries is restrictive and excludes the analysis of North-South
environmental issues including national differences in emission standards. However, this assumption carries
several advantages. First, it offers considerable analytical mileage and sharpens the intuition of main results.
Second, the assumption of symmetric countries excludes links between trade and the environment that have been
analyzed extensively by other studies: there are no gains from trade based on terms-of-trade changes; there are no
cross-country income differences; and there are no incentives for international factor movements. In other words,
the assumption of structurally identical countries highlights the environmental effects of firm heterogeneity which
is missing from the existing literature on trade and the environment.
In our model, new varieties are discovered through resource-based environmental R&D investment. Firms
engage in environmental R&D in response to government regulations with the purpose of meeting the minimum
4 In 2009, President Barack Obama announced higher emission standards requiring each manufacturer to reach an average of
35.5 miles per gallon (MPG) by 2016. The European Union has adopted the grams per kilometer car emissions standard (EU
NEDC). An et al. (2011) provide more details on policies associated with vehicle emissions.
5 The literature developing the theory of trade with heterogeneous firms includes Melitz (2003), Melitz and Ottaviano (2008),
Baldwin and Harrigan (2011), and Johnson (2012) among many others. Redding (2011) provides an excellent literature
review of theories of trade with heterogeneous firms.
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environmental quality standard.6 We view environmental R&D as a compulsory investment before any production
materializes. We assume that firms pay a fixed entry cost to invest in environmental R&D enabling them to draw
an environmental quality parameter from a common and known distribution. Each successful firm learns the
environmental quality level and faces an exogenous, government-imposed, minimum environmental-quality
standard, such as CO2 emissions. If the discovered variety does not meet this standard, the firm exits the market
immediately. Firms producing products with environmental quality equal or greater than the government imposed
standard serve the market. Additionally, we assume that the marginal cost of production increases with the level
of environmental quality. For instance, in the case of cars installing lighter materials, high-quality batteries, better
electronic components, and using more high-skilled workers raise both fuel efficiency and per-unit production
costs.
As in Melitz (2003), successful firms can engage in exporting by paying a fixed foreign-market entry cost
and incurring a per-unit trade cost. These assumptions provide an endogenous export cutoff environmental quality
level that partitions firms by export status. The government-imposed standard serves the same purpose in the
present model as the domestic fixed cost of production in the literature on heterogeneous firms and trade.
As in the case of vehicles and household appliances, consumption generates pollution. The amount of
pollution per variety is proportional to the quantity consumed adjusted by the pollution intensity. The latter
decreases with variety’s environmental quality. In other words, firms that discover products with higher
environmental quality exhibit lower pollution intensities. This assumption is consistent with evidence on cars: the
2015 Mitsubishi Mirage with fuel efficiency of 37 MPG emits 238 grams of CO2 per mile, whereas the 2015
Chevrolet Spark EV (electric) with fuel efficiency of 119 MPG emits close to zero grams of CO2.7
In the model, firms and consumers take aggregate pollution as given. Firms with larger revenues, enjoy
greater operating profits, cover fixed and variable trade costs and engage in exporting. This prediction is
consistent with evidence that within narrowly defined product categories firms earning larger revenues and profits
engage in exporting.8
One of our main findings is identifying conditions under which “cleaner” or “dirtier” products are traded.
These conditions stem from the green elasticity which increases with the intensity of consumer preferences for
environmental quality and decreases with the quality elasticity of production costs. The case of cleaner intra-
industry trade arises if consumers exhibit strong preferences (relative to costs) for environmental quality leading
to a positive green elasticity. Firms producing products with high environmental quality are larger, charge higher
6 Environmental R&D may reduce the cost of abatement or reduce the amount of polluting inputs used in the production
process, as in Bovenberg and Smulders (1995) and Xepapadeas and Zeeuw (1999).
7 See www.fueleconomy.gov, the official U.S. government source for fuel economy information.
8 See Tybout (2003) for a survey of early empirical studies documenting that exporting firms are larger and more productive.
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prices, earn greater revenues, and export their products; firms discovering products with lower environmental
quality charge lower prices, earn lower revenues and serve the domestic market only.
The case of dirty intra-industry trade arises when consumer preferences for environmental quality are
weak relative to product costs leading to a negative green elasticity. In this case, firms discovering varieties with
low environmental quality charge lower prices, earn higher revenues and profits and export their products. As a
result, the model generates “eco-dumping” in the absence of comparative advantage and international capital
movements. In other words, the model offers a novel intra-industry version of the “race to the bottom” hypothesis
based on self-selection of heterogeneous polluters where cost-leadership (as opposed to environmental quality
leadership) confers international competitive advantage to firms producing dirtier and cheaper products.
We also analyze the effects of more stringent environmental quality standards and trade liberalization on
per-capita consumption, global pollution and welfare. Trade liberalization takes the form of lower per-unit trade
costs, lower fixed costs of entering foreign markets, or more trading partners. Welfare is modeled as the
difference between per-capital consumption and global pollution. We establish that a stricter global environmental
quality standard or any form of trade liberalization increase per-capita consumption. The intuition behind this
result is analogous to the standard intuition provided by the theory of trade with heterogeneous firms: these
policies shift resources from environmental R&D and firms serving the domestic markets to exporters. As a
result, the measure of varieties available for consumption rises leading to a lower price index and an increase in
per-capita real income and per-capita consumption aggregated over all available varieties.
The effects of global environmental standards and trade liberalization on global pollution are ambiguous.
As said, these policies raise the number of consumed varieties and lower the average quantity consumed by
increasing the intensity of competition. Pollution intensity decreases with environmental quality introducing
another factor that lowers pollution. The increase in the measure of consumed varieties raises the extensive
margin of pollution whereas the decline in quantity consumed reduces the intensive margin of pollution. As a
result, the impact of trade liberalization and global standards on pollution is ambiguous.9 This ambiguity is
inherited in the welfare effects of these policies because welfare depends negatively on global pollution.
The rest of the paper is organized as follows. Section 2 discusses the contribution of our paper to related
studies. Section 3 presents elements of the model and describes the steady-state equilibrium. Section 4 studies the
effects of a more stringent environmental standard and trade liberalization on global pollution, per-capita
9 The ambiguity of trade on pollution is reflected in the empirical literature. For instance, Frankel and Rose (2005, p89) state
“The case that would give an environmentalist the greater concern is CO2. The coefficient on openness (measured by value of
trade over GDP) is positive and moderately significant” implying that trade openness increases pollution in this case. Roy
(2015) using a similar methodology, based on the gravity equation applied to a cross section of countries argues that the
elasticity of pollution with respect to intra-industry trade is substantially greater than the elasticity of pollution with respect to
trade openness. Specifically, he finds that one percent change in the index of intra-industry trade reduces CO2 emissions by at
least 5.9 percent, whereas one percent change in trade openness increases CO2 by up to 0.4 percent.
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consumption and welfare. Section 5 concludes. We relegate algebraic details pertaining to proofs of propositions
to the Appendix.
2. Related Literature
The present paper complements the theory of trade with heterogeneous firms pioneered by Melitz (2003)
by adding two novel features. First, it establishes that in the presence of a binding product quality standard, the
separation of firms by export status depends on virtually all model parameters (as opposed to just trade costs and
fixed domestic costs). Second, it shows that the effect of higher minimum quality standards and trade
liberalization on the component of welfare that does not depend on pollution is beneficial. In other words, in the
absence of pollution, higher product-quality standards improve welfare through similar channels to those
triggered by trade liberalization.
The identification of conditions that result in clean or dirty intra-industry trade contributes to two strands
of literature. First, the case of clean intra-industry trade is consistent with the Porter Hypothesis that relates
stricter environmental standards and to international competitiveness (see Popp (2005) and Xepapadeas and de
Zeeuw (1999), among others). A recent study of the European Automobile industry by Miravete, Moral and
Thurk (2014) shows that the emissions policy employed by European regulators not only promoted the diffusion
of diesel vehicles, but also increased the profitability of domestic manufactures by providing European
automakers a comparative advantage. Using standard business terminology, the case of a positive green elasticity
in our model corresponds to exploitation of competitive advantage based on benefit leadership.
Second, our paper contributes to the debate on “pollution havens” and “pollution dumping”, one version
of which states that countries with low environmental standards or comparative advantage in pollution-intensive
goods produce dirty goods which are exported to countries with higher environmental standards, or comparative
advantage in cleaner goods (Frankel and Rose, 2005; Frankel, 2009). Our model identifies an intra-industry trade
based mechanism of pollution dumping which is independent of national differences in environmental standards,
factor endowments, or movements of capital to countries with low environmental standards. In our model, in the
case of weak preferences for environmental quality, firms that produce cheaper and dirtier products export them
abroad in an environment of identical countries and a binding global environmental quality standard. These firms
earn higher profits than average industry profits (competitive advantage) in a global economy with symmetric
countries in the absence of comparative advantage and differences in national environmental standards.
Finally our paper complements Kreickemeier and Richter (2014) who propose a model of a small open
economy populated by heterogeneous firms differing in productivity (as opposed to product quality) to study the
effects of intra-industry trade on production-generated pollution. In contrast, our model focuses on consumption-
generated pollution, a global economy characterized by many countries, and the effect of minimum environmental
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quality standards. As a result, we generate conditions leading to dirty or clean intra-industry trade and take into
account the effects of policies on the measure of imported and consumed varieties. These features are absent from
their model.
3. The Model
Following the theory of trade with heterogeneous firms, we analyze a global economy consisting of 1n
structurally identical countries with 1n . As said, the assumption of structurally identical countries is admittedly
restrictive but necessary to solve the model. This assumption, which enhances the analysis and sharpens the
intuition, has been employed by a large number of studies including the pioneering article by Melitz (2003). It
highlights the effects of environmental standards on heterogeneous polluters in the absence of comparative-
advantage, international factor mobility, and income differences across countries.
Each country consists of a sole industry producing differentiated goods with labor being the only factor of
production. The aggregate supply of labor in each country, denoted by L , is fixed and remains constant over time.
3.1. Consumers
The preferences of a representative consumer are given by
U Q Z . (1)
Variable Q denotes per-capita consumption aggregated over a continuum of products and is defined by the
following Dixit and Stiglitz (1977) sub-utility function
1/
( )( ) .
qQ d
L
(2)
In Eq.(2), each variety is indexed by and denotes the set of all varieties consumed in a typical country.
Parameter 0 1 implies that the constant elasticity of substitution between any two varieties or brands is
1/ (1 ) 1 . Variable ( )q denotes aggregate consumption of brand , and ( ) 1 denotes its time-
invariant environmental quality.
Motivated by the automobile industry, we consider environmental quality as closely related to the fuel-
efficiency of different vehicles as in the US CAFÉ standard. For example, an electric vehicle is associated with a
large value of ( ) whereas a standard SUV commands a low value of ( ) . Parameter 0 is the constant
elasticity of consumer’s sub-utility with respect to environmental quality ( ) and measures the intensity of
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consumer preferences for environmental quality.10 A larger value of implies higher perceived environmental
quality and greater consumer willingness to pay for each variety.
Consumption generates pollution. The following function defines aggregate pollution (summed over all
varieties consumed in a country)
( )Z z d
, (3)
where ( )z is the amount of pollution per variety consumed and given by
( ) ( ) / ( ).z q (4)
Pollution per variety ( )z is directly proportional to consumed quantity ( )q ; and pollution intensity per variety
/ ( ) is inversely related to variety-specific environmental quality. Parameter 0 is common among all
varieties with higher values of implying higher pollution intensity; whereas higher values of environmental
quality ( ) imply lower pollution intensity. Where 0 , consumption does not generate any pollution and the
model is equivalent to a model of trade with quality heterogeneity.
Consuming varieties with higher environmental quality increases welfare through two distinct channels: it
raises utility directly (analogous to a higher product quality); and reduces pollution intensity resulting in a cleaner
environment. Based on the literature on trade and the environment, we model the second channel as an
externality: the representative consumer behaves as though her own behavior does not affect aggregate pollution.
Note that the assumption of symmetric countries implies that the level of global pollution is equal to the
exogenous number of countries times the level of national pollution. As a result, issues associated with
transboundary pollution do not arise in the present model.
Each consumer maximizes utility (1) taking aggregate pollution Z as given, subject to the budget
constraint ( )[ ( ) / ] ,p q L d E
where ( )p is the market price; E is per-capita consumer expenditure, and
L is the number of consumers in a typical country. This maximization problem yields the market quantity
demanded ( )q and expenditure ( ) ( ) ( )r p q for variety
1 ( 1)( ) ( ) ( )q ELP p ; 1 1 ( 1)( ) ( ) ( )r ELP p . (5)
10 According to a 2014 survey by the Consumer Reports National Research Center, quality, safety, performance, value and
fuel economy are the most important considerations for today’s new-car buyers. Consumers are willing to pay higher prices
and even submit to a waiting list to purchase environmentally friendly electric and hybrid vehicles.
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Variable P is now defined as the green price index, that is, the standard price index adjusted for environmental
quality
1/(1 )1
( )
( )
pP d
. (6)
Where consumers do not care about environmentally friendly products ( 0 ), the green price index
equals the standard aggregate price index, as in Melitz (2003). Firm revenue ( )r decreases with price because
each firm faces an elastic demand curve. However, for any price level, greener products enjoy greater demand and
revenues reflecting consumer demand for environmental quality.
Term ( ) / ( )p captures the effective environmental quality of variety and will play a pivotal role
in the determination of intra-industry trade. The numerator describes the consumer valuation of environmental
quality (perceived benefit) and thus the effective environmental quality is simply per-dollar perceived
environmental quality. In other words, consumer demand for a variety with environmental quality ( ) depends
on the effective environmental quality ( ) / ( )p .
3.2. Workers and Firms
As said, labor is the sole factor of production with each worker supplying one unit of labor. As a result,
labor supply is inelastic and equal to the number of consumers L . There is a continuum of firms with each firm
choosing to produce a different variety. In each country the government sets the (global) environmental quality
standard, which is denoted with . Firms must invest in environmental R&D to discover new varieties. Each
potential entrant incurs a fixed entry cost 0ef , measured in units of labor, and interpreted as the number of
R&D researchers required to discover a new variety. After incurring the said fixed cost, a firm discovers a new
variety and the embedded environmental quality by drawing parameter ( ) from a general and commonly
known distribution with positive support.
After drawing its environmental quality, a firm has to decide whether to enter the domestic and foreign
markets based on government regulations and profitability considerations. If the environmental quality of a newly
discovered variety does not meet the global (and national) environmental standard ( ( ) ), the firm exits the
market. If the new product meets the environmental standard ( ( ) ), the firm manufactures the product
without incurring any fixed production costs. We assume that the environmental standard is strictly enforced and
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abstract from compliance issues stemming from firm attempts to conceal the true value of environmental
quality.11
Manufacturing of variety entails marginal (and average) costs that increase with environmental
quality. In order to produce ( )q units of output, ( ) ( ) ( )l q units of labor are required, where 0 is
the constant elasticity of unit-labor requirement with respect to environmental quality. Thus each firm faces
constant marginal and average costs ( ) w , where w denotes the wage rate. For example, we adopt the
reasonable assumption that, all else equal, resources (and costs) required to produce an electric Nissan Leaf
delivering 114 MPGe exceed resources needed to manufacture a Honda Civic delivering 35 MPG. For the
remainder of this paper, we omit index and use the environmental quality parameter to denote a particular
variety when this practice does not create notational ambiguity.
Firms meeting the environmental standard serve the domestic market but face additional costs to enter
each foreign market. Entry into a foreign market requires per-period fixed costs 0xf measured in units of labor
and per-unit trade cost 1 . The latter is modeled in the usual iceberg fashion: units must be produced in the
country of origin in order for one unit to arrive in the destination country. Exporting costs are independent of
environmental quality .
Regardless of differences in environmental quality, each firm faces a constant elasticity demand curve, as
per Eq. (5). A firm serving the domestic market maximizes profits by taking the measure of varieties consumed
and green price index P as given. Standard calculations deliver the following pricing rules. A firm with
environmental quality sets its domestic price ( )dp and export price ( )xp in each foreign market as a
constant markup over marginal cost
( ) /dp ; ( ) /xp , (7)
where we set the wage rate equal unity ( 1w ) in Eq. (7) by choosing labor as the numeraire. A firm with
environmental quality faces greater marginal costs when serving a foreign market as opposed to serving
the domestic market because 1 . Firms producing goods with higher environmental quality charge higher
prices.12
11 In September 2015, the German automaker Volkswagen was issued a notice of violation by the US EPA after it became
known that the company had equipped vehicles powered by turbocharged direct injection diesel engines with software
programming that activated the nitrogen oxides emissions controls only during laboratory emissions testing. This reduced the
emission levels during testing below the emission levels during actual driving. Volkswagen announced plans to spend more
than $7 billion on fixing these emission violations.
12 Eq. (5) implies that each firm faces a marginal revenue function (1 1/ )MR p p which declines with quantity,
because / 0p q , and constant domestic and foreign marginal costs: MC and MC , respectively. Setting
marginal revenue equal to marginal cost in each market delivers Eq. (7). The downward sloping marginal revenue function
and constant marginal costs features ensure that the second-order conditions for profit maximization hold.
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The consumer willingness to pay and the market price depend on environmental quality. The green
elasticity reflects this dependence.
Definition 1: Let ( ) / ( )p denote the market effective environmental quality, where the profit-
maximizing price ( )p is given by Eq. (7). The green elasticity ln ( ) / ln a denotes the percentage
change in effective environmental quality ( ) brought about by one percent change in actual environmental
quality .
In the present model, the green elasticity is constant. When is positive (negative), the effective
environmental quality increases (decreases) with actual environmental quality. This property has implications for
the pattern of intra-industry trade.
The quantities of a variety with environmental quality sold in the domestic and each of n foreign
markets are given by
1 ( 1)( )dq ELP ; 1 ( 1)( )xq ELP . (8)
Total quantity ( )q produced by a firm depends on export status. A firm serving only the domestic
market produces
1 ( 1)( ) ( )dq q ELP , (9)
whereas each exporter produces
1 ( 1)( ) ( ) ( ) (1 ) ( ) (1 )d x dq q nq n q n ELP . (10)
Domestic revenue ( ) ( ) ( )d d dr p q and revenue in each of n foreign markets ( ) ( ) ( )x x xr p q are given
by
1 ( 1)( ) ( )dr EL P ; 1 1 1 ( 1)( ) ( ) ( )x dr r EL P . (11)
Firm revenue depends on export status as well and given by
1 1 1( ) ( ) ( ) (1 ) ( ) (1 ) ( )d x x x d xr r I nr I n r I n EL P , (12)
where xI is the indicator function which equals one if the firm engages in exporting and zero if the firm serves
only the domestic market; and
( )( 1) ( 1) (13)
denotes the environmental-quality elasticity of firm revenue.
Eq. (12) reveals that the green elasticity regulates the dependence of firm revenue (and operating profits)
on environmental quality. Specifically, the elasticity of revenue with respect to environmental quality
ln ( ) / lnr is constant and equal to ( 1) , where 1/(1 ) 1 is the elasticity of substitution
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between two varieties and the price elasticity of demand for each variety. As a result, the sign of green elasticity
is the same as the sign of ln ( ) / lnr . The intuition behind this property is as follows. Eq. (5)
indicates that an increase in environmental quantity raises the quantity demanded and firm revenue for any given
price. However, the effect of environmental quality on the optimal firm revenue is ambiguous: first, for a given
price, an increase in by one percent raises firm revenue directly by ( 1) percentage points; second, one-
percent increase in raises the profit-maximizing price by percentage points (see Eq. (7)) and thus lowers
firm revenue by ( 1) percentage points because each firm faces an elastic demand curve. Consequently, the
overall effect of environmental quality on firm revenue is ambiguous and depends on green elasticity . If
, where consumers have a strong preference for environmental quality, the green elasticity is positive and
cleaner, more expensive products enjoy larger revenues. If , where consumers care more about the costs of
environmental quality, the green elasticity is negative and dirtier, cheaper products enjoy larger revenues.
We continue the analysis by stating the properties of profit flows. Standard calculations imply that
domestic profits and profits from exporting are proportional to corresponding revenues. Specifically, for a firm
which meets the global environmental standard ( ), domestic profit flow ( )d is given by
( ) ( ) /d dr , (14)
and profit flow ( )x earned from sales in each of n foreign markets is
( ) ( ) /x x xr f , (15)
where xf is the fixed cost of foreign-market entry. As a result, total per-period profit ( ) is given by
( ) ( ) ( )d x xI n , (16)
where xI assumes the value of zero if the firm serves the domestic market only and the value of one if the firm
serves all export markets. The following lemma summarizes the basic findings so far.
Lemma 1: Active firms charge prices which increase with environmental quality. If the green elasticity is
positive, then firms discovering products with higher environmental quality earn larger revenues and profit flows.
If the green elasticity is negative, then firms discovering products with lower environmental quality earn larger
revenues and profit flows.
Since exporting involves fixed costs, only the larger and most profitable firms meeting the global
environmental standard serve all foreign markets. Lemma 1 states that the green elasticity determines the
environmental content of intra-industry trade, as will be discussed later.
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The amount of pollution ( )z emitted by a firm depends on export status as well. A firm discovering a
product with environmental quality emits
1 ( 1) ( 1)( ) ( ) ( ) (1 ) ( ) (1 )d x x x d xz z I nz I n z I n ELP , (17)
where xI is the export-status indicator function. The effect of environmental quality on pollution per variety is in
general ambiguous. An increase in quality reduces pollution directly, as indicated by Eq.(4), but has an
ambiguous effect on quantity consumed ( )q , as established by Eq. (10). Thus, if the green elasticity is negative
firms with higher quality produce less and generate less pollution. If the green elasticity is positive and
sufficiently high, then firms with greener products produce more units than firms with dirtier products and thus
contribute to pollution more.
3.3. Entry Decisions
Following the pioneering work of Melitz (2003), suppose that in each country there are large numbers of
prospective ex-ante identical entrants. A firm engaged in environmental R&D incurs fixed entry cost 0ef . This
initial cost allows it to draw its environmental quality parameter from a common and known distribution ( )g
with positive support over (0, ) and with continuous cumulative distribution ( )G . After observing its
environmental quality level, each firm decides whether to exit the market immediately or start producing.
Countries are identical and thus every country sets the same environmental standard, expressed as a minimum
environmental quality level 1 . The global standard is strictly enforced and serves as the domestic cutoff
quality (productivity) level in the theory of heterogeneous firms. If a firm discovers a product with environmental
quality , then the government does not allow it to enter the market. If a firm discovers a product with
environmental quality equal to or greater than the standard , then it is allowed to enter the market and thus
earns positive operating (and total) profits.
After learning its environmental quality level , a firm must decide whether or not to export by incurring
a fixed export cost 0xf and a per-unit trade cost 1 . The export cutoff level of environmental quality x is
determined implicitly by setting the flow of profits from exporting equal to zero
( ) ( ) / 0 ( )x x x x x x x xr f r f . (18)
Firms earning positive profits from exporting ( ( ) 0x or ( )x xr f ) serve all foreign markets. However,
whether firms producing greener or dirtier products become exporters depends on the sign of green elasticity as
stated in Lemma 1.
The following proposition summarizes our findings regarding the environmental pattern of intra-industry
trade.
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Proposition 1: Firms with higher environmental quality products ( ) incur higher marginal costs and
charge higher prices. The pattern of intra-industry trade depends on green elasticity as follows:
(i) If the green elasticity is positive ( 0 ) and firms face sufficiently high foreign-entry market costs
xf , then the export cutoff environmental quality level is strictly greater than the global
environmental standard ( x ); firms producing products with low environmental quality such
as x earn lower profits and serve only their domestic market; and firms producing products
with high environmental quality such as x earn higher profits and serve their domestic and all
foreign markets.
(ii) If the green elasticity is negative ( 0 ) and firms incur sufficiently low foreign-market entry costs
xf , then the export cutoff environmental quality level is strictly greater than the global
environmental standard ( x ); firms producing varieties with low environmental quality such
as x earn higher profits and serve their domestic and foreign markets; and firms producing
varieties with high environmental quality such as x earn lower profits and serve only their
domestic market.
Proof: Please see the Appendix.
Proposition 1 highlights the role of green elasticity in determining the environmental pattern of intra-
industry trade. In the case of positive green elasticity and sufficiently high trade costs, firm global competitive
advantage stems from benefit (as opposed to cost) leadership. Consumers have strong preferences for
environmental quality, and thus firms with cleaner, more expensive products earn higher profits, incur both fixed
and variable trade costs and export their products. Firms discovering dirtier products, charge lower prices and
serve only the domestic market because they cannot pay the high trade costs of entering and serving foreign
markets.
In contrast, when the green elasticity is negative and trade costs sufficiently low, the model generates dirty
intra-industry trade. In this case, consumers care more about costs than perceived environmental benefits,
generating favorable conditions for cost (as opposed) to benefit leadership as a strategy to achieve global
competitive advantage. Consequently, firms discovering products with low environmental quality charge lower
prices and enjoy higher operating profits, whereas firms discovering cleaner products charge higher prices and
earn lower profits. The latter cannot cover the cost of exporting and serve the domestic market only. As a result,
for sufficiently low trade costs, a negative green elasticity generates dirty intra-industry trade. In other words,
15
when the green elasticity is negative, the model generates intra-industry “eco-dumping” where the environmental
content of trade is lower than the environmental content of good produced by firms serving the domestic market
only.
Where the green elasticity is zero (that is, ), profit-maximizing revenues (and profit flows) are
independent of environmental quality. In this special “razor’s edge” case, all firms export their products for a
sufficiently low value of the global environmental standard; whereas, for a sufficiently high value of the global
environmental standard, all firms serve their domestic markets only. This implication is unrealistic and
inconsistent with empirical studies asserting that some firms export and others serve only their domestic markets
within narrowly defined product categories. We therefore focus on and analyze the cases of clean and
dirty intra-industry trade.
Proposition 1 generates the partition of firms into exporters and non-exporters which depends on per-
capita expenditure E and the green price index P . These variables are endogenous. This means that the previous
discussion relating the pattern of intra-industry to the sign of green elasticity does not take into account firm-entry
considerations. In Section 2.6, we will describe the steady-state equilibrium conditions and establish the general-
equilibrium validity of Proposition 1.
Next, we analyze the entry decision of a typical firm. Every incumbent firm faces a constant probability
of default ( 0 1 ) in each period caused by a stochastic shock. In the present context, this stochastic shock can
be interpreted as changing tastes that eliminate the demand for a particular variety. Since firm default is
uncorrelated with environmental quality, the exit process is independent of the distribution of the latter. The
probability of drawing an environmental quality level is governed by density function ( )g . As a result, the ex-
ante probability of successful entry is given by 1 ( )inp G . The density of the distribution of environmental
quality draws meeting the environmental standard, which is denoted by ( ) , is the conditional density of ( )g
on the interval , defined by
( )
( )1 ( )
g
G
. (19)
The ex-ante probability that an incumbent firm becomes an exporter equal the fraction of exporters and is given
by
1 ( )
1 ( )
xx
Gp
G
. (20)
16
3.4. Aggregation
Aggregation provides expressions for various components of ex-ante profits that are needed to establish
the general-equilibrium properties of the model. Let pM denote the measure of varieties produced, xM the
measure of exported varieties, and cM the measure of varieties available for consumption in each country. These
measures are related to each other as follows.
x x pM p M ; (1 )c p x x pM M nM np M . (21)
Let p denote an index of environmental quality of domestically produced goods. This quality index is
defined by
1
1( ) ( )
1 ( )p g d
G
, (22)
where ( 1) 0 is the quality elasticity of firm revenue defined in Eq. (13). Because 1 , if the green
elasticity is positive ( , 0 ), then p has identical properties to those associated with the average firm
productivity in Melitz (2003). If the green elasticity is negative ( , 0 ), then p corresponds to the weighted
harmonic mean of effective qualities of all domestically produced varieties, as in Dinopoulos and Unel (2013).
The quality index p depends on the global environmental standard and density ( )g of environmental quality.
Let x denote the average environmental quality of exports, which is defined by
1
1( ) ( )
1 ( ) xx x
x
g dG
. (23)
The average environmental quality of varieties available for consumption in a country is denoted with c and
defined by
1
1p xc p x
c c
M nM
M M
. (24)
The first term inside the square brackets corresponds to domestically produced varieties and the second term
corresponds to imported varieties.
Lemma 2: The average environmental quality of produced varieties p is strictly greater and increases with the
environmental standard (p and / 0p ). If the green elasticity is positive ( 0 ), then the average
environmental quality of exports x is strictly greater and increases with the export cutoff environmental quality
17
( x x and / 0x x ). If the green elasticity is negative ( 0 ), then the average environmental quality of
exports x is strictly smaller and decreases with the export cutoff environmental quality ( x x and
/ 0x x ).
Proof: Please see the Appendix.
Green price index P , aggregate revenue R and aggregate quantity Q in any country may be written as
functions of the average level of environmental quality c and the measure of varieties available for consumption
cM . The Appendix provides algebraic details.
1/(1 ) /c cP M ; ( )c d cR M r ; 1/( 1)
c cQ M . (25)
The market equilibrium in any country is isomorphic to the equilibrium with cM identical firms, each of which
produces a variety with environmental quality c .
Finally, expected revenue r and profit earned by a representative firm serving the domestic and
foreign markets are given by
( ) ( )d p x x xr r p nr ; ( ) ( )d p x x xp n . (26)
3.5. Free Entry
A firm producing a variety with environmental quality earns operating profit ( ) and faces a
constant probability of death in each period. Following the literature on trade with heterogeneous firms, we
assume that the discount (and interest) rate equals zero. As a result, firm market value is given by
0
( )( ) max 0, (1 ) ( ) max 0,t
t
v
, (27)
where the second equality is based on the property that environmental quality is time invariant and thus the firm
earns the same profit flow each period. The firm meets the environmental standard and enters the market
successfully with probability 1 ( )G . As a result, expected net benefits of conducting environmental R&D are
equal to ex-ante expected firm value 1 ( )G , where / is the (ex-post) value of a successful entrant,
and is the profit flow ( ) ( )d p x x xp n , defined in Eq. (26).
18
Free entry into environmental R&D leads to zero expected net benefits: expected benefits of entry
1 ( )G must equal the fixed R&D entry cost ef yielding the free-entry condition
1 ( )ef G . (28)
The LHS of Eq. (28) is expected cost of environmental R&D and its RHS is average firm profit. Average firm
profit is therefore determined by firm default rate , fixed cost of environmental R&Def , and the global
environmental standard . Ceteris paribus, a higher environmental standard lowers the probability of
successful entry1 ( )G and requires higher profit flow to restore free-entry condition(28). Similar
considerations apply to the rate of default and entry costef : higher expected R&D cost
ef requires higher
profit flow .
3.6. Equilibrium
At the steady-state equilibrium, the zero-profit condition(18), determines the relationship between the
average profit per firm and the export cutoff environmental qualityx .
Combining Eq. (11) and Eq. (14) yields
( ) ( )
( ) ( )
d p d p p
d x d x x
r
r
; ( )
( )
x x x
x x x
r
r
. (29)
We can express the average profit flow , which is defined by Eq. (26), as
1 1 ( )1
1 ( )
p x xx x
x x
Gf nf
G
, (30)
where x is a function of x .13 Substituting Eq. (30) into Eq. (28) yields the following zero-profit environmental
R&D condition
/ ( )e x xf f F , (31)
where
1( ) ( ) ( ) [1 ( )]x
x x x xF g d n g d G
. (32)
13 The first and second terms in the right-hand-side (RHS) of (30) are equal to the corresponding terms in the RHS of in
(26). Eq. (11) and Eq. (18) imply 1 1( ) ( ) /d x x x xr f . Substituting ( )d x in Eq. (29) yields the first term in the
RHS of Eq. (30). Eq. (15) implies . Substituting from Eq. (29), [1 ( )]/[1 ( )]x xp G G and
( )x x xr f from Eq. (18) delivers to the second term in the RHS of Eq. (30).
19
The environmental R&D condition determines the general-equilibrium export cutoff levelx . The LHS of
Eq. (32) equals per-period expected fixed environmental R&D costs expressed in units of foreign-market entry
costxf ; and ( )xF equals per-period expected profits, expressed in units of foreign-market entry costs
xf , earned
by a firm engaged in environmental R&D. It can be easily established that expected profits decrease
monotonically with export cutoff quality level x if and only if the green elasticity is positive:
/ 0 0xF .14
The intuition behind the sign of ( )xF is as follows. Observe that per-period firm profit is higher for
firms serving both the domestic and foreign markets than for firms serving only their domestic markets, as
indicated by Proposition 1. In the case of positive green elasticity, firms producing products with environmental
quality higher than the export cutoff level ( x ) become exporters and earn higher profits. In this case, an
increase in x reduces the likelihood that a firm will earn higher profits by becoming an exporter and increases
the likelihood that the firm will earn lower profits by serving the domestic market only. As a result, if 0 , then
an increase in x reduces per-period expected (average) profits ( )xF . If 0 , then firms producing products
with environmental quality which is lower than the export cutoff level x earn higher profits and become
exporters. In this case, an increase inx increases the range of environmental quality generating higher profits and
reduces the likelihood of lower profits associated with serving only the domestic market. As a result, if 0 then
an increase in x raises per-period average firm profit ( )xF .
The environmental R&D condition / ( )e x xf f F determines the export cutoff level as follows.
Consider first the case of 0 , where ( )xF decreases with x . The R&D condition must hold at the minimum
environmental standard, ( / ( )e xf f F ). Thus if x , then all active firms export and obtain maximum
expected profits equal to ( )F . If / ( ) ( )e x xf f F F , then the export cutoff level is higher than the global
environmental standard ( x ); firms discovering environmental quality products exceeding the export cutoff (
x ) become exporters; and firms with environmental quality products below the export cutoff level and above
the global environmental standard ( x ) serve their domestic market only.
Similar reasoning applies to the case of negative green elasticity. In this case, evaluating the R&D
condition at the global standard where x implies that all firms obtain minimum ex ante profit equal to
14 Formally, the partial derivative of the RHS of Eq. (32) with respect to x equals
( 1) 1( ) / ( ) ( )x
x x xF g d n g d
implying that ( / ) ( )xsign F sign .
20
( , )F . In this case, all firms serve the domestic market and there is not separation between local firms and
exporters. Since expected profit increases with x in this case, if ( ) / ( )e x xF f f F (that is, for sufficiently
high expected entry costs /e xf f ), the export cutoff level is strictly greater than the global standard ( x ).
Firms with environmental quality products higher than the export cutoff ( x ) serve the domestic market; and
firms discovering products with environmental quality between the export cutoff level and the global standard (
x ) engage in exporting.
Fig. 1 illustrates the general-equilibrium solution to the export cutoff level x in the case of positive
green elasticity by plotting the LHS and RHS of the environmental (zero-profit) R&D condition (31) as functions
of x . The LHS is independent of x and is shown by horizontal line /e xf f . Fig. 1 illustrates the graph of
( )xF which is downward sloping in the case of positive green elasticity. The intersection of the vertical line
passing through and curve ( )xF at point A determines ( )F . In Fig.1, /e xf f is strictly lower than ( )F .
As a result, the intersection of /e xf f and curve ( )xF determines the equilibrium export cutoff x . It is
obvious from Fig. 1 that there exists a sufficiently high level of xf such that the export cutoff quality level
x
exceeds the global environmental standard .
Figure 1. Determination of export cutoff x when 0 .
In the case of negative green elasticity ( 0 ), the graph of ( )xF (not shown in Fig.1) has positive
slope and passes through point A. Thus for a sufficiently high level /e xf f , such as ( ) /e xF f f , the
( )F A
/e xf f
21
horizontal line is located above point A. In this case, the unique intersection between line /e xf f and upward-
sloping curve ( )xF determines the general-equilibrium value of export cutoff x which is greater than the
global environmental standard . These considerations imply that Proposition 1 holds in general equilibrium.
Proposition 2: There exists an export cutoff level which is unique and strictly greater than the global
environmental standard ( x ) satisfying equation (31) under the following parameter restrictions: if the green
elasticity is positive (negative), then the ratio of expected entry costs to foreign-market entry costs /e xf f
must be strictly lower (greater) than ( )F . The intra-industry trade pattern described by Proposition 1 holds in
general equilibrium.
The equilibrium export cutoff environmental quality level x and global environmental standard
determine the average environmental quality levels of exports x , domestically produced goods p , and goods
available for consumption c . Equilibrium probabilities inp and xp are determined as well.15
Proposition 2 identifies the conditions providing separation between domestic firms and exporters. These
conditions involve more parameters than those identified by the traditional theory of trade with heterogeneous
firms. For instance, in Melitz (2003) the domestic cutoff quality level d is given by setting the ex-post flow of
domestic profits equal to the fixed costs of production ( )d d f , where f denotes the fixed costs of entering
the domestic market. Combining this equation with (11) and (18) yields the standard condition for the partitioning
of firms by export status which occurs if and only if 1
xf f . In contrast, in the present model the presence of
a minimum (environmental) quality standard acts as the exogenous domestic cutoff quality level and implies that
several additional parameters affect the partitioning of firms by export status. These additional parameters include
, ,ef and parameters regulating the distribution of environmental quality.16
4. Effects of Environmental Standards and Trade Liberalization
In this section we analyze the effects of the global environmental standard , and the impact of three
types of trade liberalization: an increase in the number of trading partners n ; a reduction in variable trade costs ;
15 The determination of the remaining endogenous variables such as the measure of varieties produced and consumed in each
country, and aggregate profits is standard and omitted here based on space considerations.
16 Proposition 2 applies to markets with binding product quality standards independently of pollution considerations. These
quality standards include safety and health-hazard standards applied to pharmaceuticals, many agricultural products, and
construction materials.
22
and a reduction in foreign-market entry costs xf . We begin the analysis by establishing the impact of these
parameters on the export cutoff level of environmental quality x .
Lemma 3: The equilibrium cutoff level of export environmental quality x :
(i) declines (increases) with the global environmental standard if the green elasticity is positive
(negative);
(ii) decreases (increases) with a reduction in per-unit trade costs , if the green elasticity is positive
(negative);
(iii) decreases (increases) with a reduction in foreign-market entry costs xf , if the green elasticity is
positive (negative);
(iv) increases (decreases) with the number of trading partners n , if the green elasticity is positive
(negative).
Proof: Please see the Appendix.
The intuition behind Lemma 3 can be described with the help of zero-profit condition (31). A more
stringent environmental standard leads to lower level of average profits because it decreases the probability
of successful entry. Similarly, trade liberalization in the form of lower per-unit trade costs or lower foreign-
market access costs xf reduces average profit by lowering the equilibrium domestic profit flow 1
d xf . An
initial reduction in average firm profit requires a compensating increase in the export cutoff quality x to restore
the zero-profit condition. Thus if the green elasticity is positive, then a reduction of x raises average firm profit;
whereas if the green elasticity is negative, then an increase in x is required to increase average firm profit. In
contrast, an increase in the number of trading partners n raises average profits by increasing the demand (as
opposed the supply) for exports. The initial increase in average profits is reversed by raising (reducing) the export
cutoff level x if the green elasticity is positive (negative).
Armed with Lemma 3, we proceed to analyze the impact of global environmental standard and
globalization on per-capita consumption Q , aggregate (and per-capita) pollution Z , and welfare W Q Z . Per
capita consumption is given by the Dixit-Stiglitz (1977) sub-utility, as indicated by Eq. (2)
1/ 1/( 1)
( )( ) x
x
q LQ d
L f
, (33)
where the last expression is derived in the Appendix (please see Eq. (A15)). Per-capita (and aggregate) pollution
Z can be written
23
( 1) ( 1)( ) ( )
x
p x
c cc
M ML nZ d d
M M
. (34)
Eq. (34) was derived by aggregating Eq. (17) over all active firms and using Eq. (21) and Eq. (25). As a result,
per-capita welfare can be expressed as
( 1) ( 1)1/( 1) ( ) ( )
x
p x
c cx
x c
M MnL d d
M MLW
f
. (35)
The following proposition states the effects of a higher environmental standard and trade liberalization
Proposition 3: A more stringent environmental standard ( ), or trade liberalization in the form of a reduction
in per-unit trade costs ( ), lower foreign-market access costs ( xf ), and greater number of trading partners (
n ) has the following affects:
(i) it increases per-capita consumption Q ;
(ii) and has ambiguous effects on aggregate pollution Z and thus welfare W .
Proof: Please see the Appendix.
We provide the following intuition behind Proposition 3. A higher environmental standard and any form
of trade liberalization shifts resources from domestic R&D and domestic firms towards exporting firms. This
resource shift reduces the measure of produced varieties and increases the measure of traded varieties. The latter
effect dominates resulting in more varieties available for consumption, a lower green price index, a higher real
wage and a higher level of per-capita consumption. In other words, in the absence of pollution ( 0 ), higher
quality standards and trade liberalization increase welfare, as in Melitz (2003).
The presence of consumption-based pollution alters the standard beneficial welfare effects of trade
highlighted by the theory of trade with heterogeneous firm. It is apparent from Eq. (35) that, depending on the
parameter values such as a sufficiently large pollution intensity or number of consumers L , per-capita welfare
W can be either positive or negative. In addition, a more stringent environmental standard or any facet of trade
liberalization affects the level of pollution through several channels. Consider, for instance, the impact of a higher
global environmental standard. According to Lemma 3 a higher decreases expected profits and the reward to
environmental R&D. This leads to a lower measure of successful firms and produced varieties in each country.
This leads to a shift of resources from firms serving the domestic market only to exporting firms and an increase
in the measure of traded varieties resulting in more varieties available for consumption (and more pollution). The
increase in varieties available for consumption intensifies competition and lowers the quantity consumed per
24
variety. This channel reduces pollution since it depends on aggregate quantity consumed. Finally, an increase in
has an ambiguous effect on average environmental quality which is inversely related to aggregate pollution.
More formally, the dependence of aggregate pollution Z on the export cutoff x is highly non-monotonic. As a
result, the effect of a higher environmental standard on pollution and thus welfare is in general ambiguous. The
appendix establishes formally that this ambiguity cannot be eliminated even in the special case where the global
environmental standard is sufficiently high inducing all firms meeting the standard to become exporters ( x ).
Trade liberalization affects pollution primarily through changes in the export cutoff quality level x which
has an ambiguous effect on pollution for reasons stated in the previous paragraph. Lower variable trade costs,
lower fixed trade costs, or more trading partners increase profitability of exporting, raise the number of varieties
consumed (increasing pollution), reduce the quantity consumed per variety (leading to lower pollution), and have
an ambiguous impact on average quality of consumed varieties. The ambiguous effect of trade liberalization on
aggregate pollution is translated into an ambiguous welfare effect.
5. Conclusions
This paper builds a simple monopolistic competition model of trade with heterogeneous polluters. Firms
in this model charge constant markups over marginal costs and prices that are positively related to firm-specific
environmental quality level. Consumption of varieties generates pollution. The model addresses the effects of
environmental standards and trade liberalization on intra-industry trade patterns, global pollution and welfare.
Trade liberalization takes the form of greater number of trade partners and lower fixed and variable trade costs.
The environmental content of intra-industry trade depends on model parameters captured by the green
elasticity. When consumer preferences for environmental quality are strong relative to the costs of producing
cleaner products, firm discovering cleaner products are more profitable and engage in exporting. In contrast, when
consumers have weak preferences for environmental quality, firm discovering dirtier products are more profitable
and become exporters. As a result, the model generates intra-industry “eco dumping” in the absence of
comparative advantage, differences in environmental standards across countries, and international factor
movements.
Stricter global environmental standards drive inefficient firms out of the market and induce entry into foreign
markets. This leads to higher revenues and profits for all firms. The effects of higher environmental standards on
aggregate pollution and welfare are ambiguous. Trade liberalization reduces profits and revenues of firms serving
the domestic market; raises revenues and profits of exporting firms; and has an ambiguous effect on pollution and
welfare.
25
The proposed analytical framework can be used to address a number of additional issues. For example,
the ambiguous welfare effects of trade liberalization and environmental standards suggest the existence of
optimum global standards and trade policies. Instead of consumption-based pollution one can introduced
production based pollution. Finally, relaxing the assumption of symmetric countries would permit the analysis of
country-specific environmental standards and trade policies. These issues are beyond the scope of the present
paper and constitute fruitful avenues for future research.
26
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28
Appendix
A.1. Proof of Proposition 1
Lemma 1 implies that export revenue ( )xr increases (decreases) in environmental quality if and only
if 0 ( 0 ). Substitute Eq. (11) into Eq. (18) to obtain 1( ) ( ) /d d xr f . This equation reveals the
following. If the level of trade barriers 1
xf
equals the minimum level of operating profit
( ) ( ) / 0d d xr f , then the global environmental standard solves Eq. (18) and thus the export cutoff
coincides with the global environmental standard and all active firms export, i.e., x . In the case of positive
green elasticity ( 0 ) operating profits increase with environmental quality. Therefore if the level of trade
barriers 1
xf is strictly greater than ( )d , then the export cutoff environmental quality level is strictly greater
than the environmental standard ( x ). In this case, products with high environmental quality are exported,
products with intermediate environmental quality are sold in the domestic market, and products with
environmental quality below the global standard are not produced.
In the case of negative green elasticity ( 0 ), where operating profits decrease with environmental
quality, operating profit flow reaches its maximum when evaluated at the environmental standard, that is,
( ) ( )d d for . The aforementioned reasoning implies the following: if 1( )d xf , then the
export cutoff coincides with the environmental standard ( x ), and all firms serve the domestic market only.
Firms with environmental quality levels greater than the global standard earn negative profits from exporting. As
a result, if the level of trade barriers 1
xf is strictly less than ( )d , the export cutoff quality level is strictly
greater than the domestic cutoff quality level (global environmental standard), that is, x . In this case, firms
with low environmental quality products ( x ) engage in exporting, whereas firms with higher
environmental quality products ( x ) serve the domestic market only.
A.2. Proof of Lemma 2
Let parameter ( 1) denote the elasticity of firm revenue with respect to environmental quality .
Because 1 the sign of is the same as the sign of green elasticity . Every active firm must meet
the environmental standard, that is,1 . As a result, we have if 0 and if 0 .
29
Consider first the case of a positive green elasticity ( 0 ). Substituting into the definition of
p , in Eq. (22), yields
1 1
( ) ( )1 ( ) 1 ( )
p g d g dG G
, (A1)
which leads to p . Let
1( ) ( )
1 ( )H g d
G
. Differentiating equation Eq. (22) yields
(1 )/ 1
( )p H
H
, (A2)
where
2
( ) 1 ( ) ( ) ( ) ( )1
[1 ( )]1 ( )
pg G g d g gH
GG
. (A3)
Because 0 and p
, we have (1/ )( / ) 0H . As a result, an increase in the global standard
raises the average environmental quality of produced varieties ( / 0p ). In the case of negative green
elasticity ( 0 ), inequality (A1) is reversed implying p
. Thus inequality (1/ )( / ) 0H holds, and
therefore / 0p . In sum, the average quality of domestically produced goods increases with the global
environmental standard independently of the sign of the green elasticity.
The average export environmental quality x is defined in Eq. (23). In the case of positive green
elasticity ( 0 ), the export cutoff x
is the minimum of all export quality levels (x ). As a result,
inequality x
holds. Combining this inequality with Eq. (23) yields
1 1( ) ( )
1 ( ) 1 ( )x xx x x
x x
g d g dG G
, (A4)
leading to x x .
Let 1
( ) ( )1 ( ) x
x
x
J g dG
. Differentiating Eq. (23) delivers
(1 )/ 1
( )x
x x
JJ
, (A5)
where
2
( ) 1 ( ) ( ) ( ) ( )1
[1 ( )]1 ( )
xx x x x x x x
x xx
g G g d g gJ
GG
. (A6)
30
Since x x
and 0 expression (A6) is positive. Thus if the green elasticity is positive ( 0 ), then an
increase in the export cutoff quality level raises the average quality of exports ( / 0x x ).
Finally, consider the case of negative green elasticity ( 0 ), where the export cutoff is the maximum of
all export quality levels, i.e.x . In this case, where ( 1) 0 , the following inequality holds: x
.
This implies that Eq. (A4) holds leading to inequality x x
. As a result, expression (A6) is negative and,
therefore, / 0x x . In words, if the green elasticity is negative ( 0 ), then the average environmental
quality of exports x declines with the export cutoff level
x .
A.3. Derivation of aggregate variables P , R and Q
Using Eq. (7), the green price index P (given by Eq. (6)) can be written as
1/(1 )1
1 1( ) ( )
xp xP M d n M d
1/(1 )1/(1 )
1( ) ( )x
pc x
c c
MM Md n d
M M
(A7)
1/(1 )1/(1 )
1
pc xp x
c c
MM Mn
M M
1/(1 ) / .c cM
Under intra-industry trade, aggregate revenue 0
( ) ( )R r M d
can be written as
( ) ( ) ( ) ( )x
d p x xR r M d n r M d
. Using Eq. (11) and Eq. (12) delivers
1( ) ( ) ( ) ( )
xd c p d c x
c c
nR r M d r M d
1
( )( ) ( )
x
pd c xc
c cc
Mr MnM d d
M M
(A8)
( )c d cM r .
31
Aggregate quantityQ , which is defined by Eq. (2), can be written as
1/1 ( ) 1 ( )( ) ( ) ( ) ( )
xp xQ P M d n P M d
1/
( 1)
1( ) ( )
xp xP M d n M d
1/
( 1)
c cM P
(A9)
/( 1) ( 1) ( )
c cM P
1/( 1) .c cM
A.4. Proof of Lemma 3
Using Eq. (32), the zero-profit R&D condition (31) can be written as
11 ( ) ( ) ( )x
ex x
x
fG n g d n g d
f
. (A10)
Differentiating Eq. (A10) with respect to environmental standard yields
1
1
( )
1 ( )
x
ex x
x
d g
d fG n
f
. (A11)
As a result /xsign d d sign because ( 1) . This proves part (i) of Lemma 3.
Differentiating Eq. (A10) with respect to per-unit trade costs , foreign-market entry costs xf , and the number of
trading partners n , respectively, delivers the following expressions:
2
1
( 1) ( )
1 ( )
x
ex x
x
g dd
d fG n
f
; (A12)
21 ( )
x e x
x e x x x
d f
df f f n G f
; (A13)
1
1 ( )
1 ( )
x x xx
ex x
x
Gd
dn fG n
f
. (A14)
32
Lemma 2 implies that x x
. As a result, the sign of Eq. (A12), Eq. (A13) and Eq. (A14) is the same as
the sign of green elasticity : ( / / ( / )x x x xsign d d sign d df sign d dn sign ). This proves parts
(ii), (iii) and (iv) of Lemma 3.
A.5. Proof of Proposition 3
Aggregate consumption, as indicated in Eq. (A9), is given by 1/( 1)
c cQ M . Eq. (11) implies
1
( )
( )
d c c
d x x c x
r L
r M f
; where the last equality stems from national income identity ( )d c cr M L and use
of Eq. (11) and Eq. (18) yielding 1( )d x xr f . As a result, 1
xc
c x
L
M f
, which implies
1/( 1)
xc
c x
L
M f
.
Per-capita consumption can then be written as
1/( 1)
x
x
LQ
f
. (A15)
Differentiating per-capital consumption (A15) with respect to yields
1/( 1)
1 xx
x
ddQ L
d d f
. (A16)
Substituting Eq. (A11) delivers
1/( 1)( 2) ( )
0( 1)
[1 ( )]
x
x ex
x
dQ L g
d f fG n
f
. (A17)
As a result, per-capita consumption increases with a stringent global environmental standard.
Differentiating aggregate consumption (A15) with respect to n yields
1/( 1)
1 xx
x
ddQ L
dn f dn
, (A18)
and substituting Eq. (A14) yields
1/( 1)
[1 ( )][ ]0
( 1)[1 ( )]
x x xx
x ex
x
GdQ L
dn f fG n
f
, (A19)
33
which establishes that per-capita consumption increases with the number of trading countries.
Differentiating aggregate consumption (A15) with respect to yields
1/( 1)
21x x
x x
ddQ L
d f d
, (A20)
where
1 ( )
1 ( )
x
x ex x
x
g dd
d fG n
f
.
Using R&D condition (31), this expression becomes
1
1
( )1
( ) ( )x
x
x
g dd
d g d n g d
. (A21)
Therefore globalization causes by a decline in per-unit trade costs increases per-capita consumption ( / 0dQ d ).
Differentiating aggregate consumption (A15) with respect to xf yields
1/( 1)
1/( 1) 111
( 1)
x xx x
x x x
d fdQ Lf
df df
, (A22)
where
11 ( )
x x e
x x e x x
d f f
df f n G f
. Therefore a reduction in fixed foreign market entry costs raises
aggregate consumption ( / 0xdQ df ).
The effects of environmental quality standards and trade liberalization on pollution are ambiguous. As Eq.
(34) indicates, this ambiguity stems from the highly non-monotonic relationship between pollution Z and the
export cutoff quality x . This relationship depends on the effect of the latter on average quality of varieties
available for consumption, the share of traded varieties and properties of the conditional density function.
We illustrate formally this property in the (unrealistic) case where the environmental standard is
sufficiently high so that all successful firms export ( x ): the measure of exported varieties equals the
measure of produced varieties ( x pM M ); and Eqs. (22) and (24) imply
11(1 )( )
[1 ( )]
p
c
c
M ng d
M G
.
Substituting this expression and ( ) ( ) / [1 ( )]g G in Eq. (34) delivers
34
( 1)
1
(1 ) ( )
(1 ) ( )x
L n g dZ
n g d
(A23)
Differentiating (A23) with respect to yields
( 1) ( 1)
21
(1 ) ( ) ( ) ( )
(1 ) ( )
x
L n g g d g dZ
n g d
(A24)
which is negative as 1 and positive for sufficiently large values of . In other words, even in the special
case where all firms export, the effect of stringent environmental standards on pollution is ambiguous. This
ambiguity carries over in the more general and realistic case where only a subset of firms export.